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Abstract
In this paper, a 3-dimensional photoelectron/ion momentum spectrometer (reaction microscope) combined with a table-top attosecond beamline based on a high-repetition rate (49 kHz) laser source is presented. The beamline is designed to achieve a temporal stability below 50 attoseconds. Results from measurements on systems like molecular hydrogen and argon dimers demonstrate the capabilities of this setup in observing the attosecond dynamics in 3D while covering the full solid angle for ionization processes having low cross-sections.
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1. Introduction
Photoionization studies on atoms and molecules have been revolutionized since the first measurement involving the generation and characterization of attosecond pulses two decades ago [1]. Attosecond pulses have since then been instrumental in observing the ultrafast electron dynamics in atoms and molecules. Although they were initially limited to atomic systems in the gas phase only, attosecond pulses now aid the understanding of dynamics in systems of increasing size and complexity such as liquids [2] and solids [3].
XUV attosecond pulses are created through the process of high-harmonic generation (HHG) [4] from femtosecond IR pulses. This has been studied extensively with a variety of HHG targets over the years [5], in order to obtain photon energies up to 100 eV or more. In parallel, femtosecond laser systems have also undergone sophistication in terms of pulse energies and wavelength tunability. Most schemes utitilize Ti:Sapphire laser oscillators or amplifiers as the starting point. These systems deliver the necessary pulse energy for HHG but they are typically limited to repetition rates of only a few kHz.
To successfully perform either single- or multi-coincidence photoelectron/-ion spectroscopy of atomic or molecular targets, generic Ti:Sapphire systems fall short considering that many processes of interest have moderate cross-sections ($\approx$ 10 kBarn). This often results in measurements lasting several days to obtain a statistically significant number of data points. To drastically shorten the data acquisition time, novel laser systems providing pulses at repetition rates of 100 kHz or more have been developed in the recent years [6–9], which have been used for HHG. These include fiber-based amplifiers e.g. [6], nonlinear post-compression of thin-disk lasers [7] or OPCPA based systems such as the one described in [9], used to perform pump-probe experiments in [10]. With pulse energies comparable to those from Ti:Sapphire systems, these fiber-based systems are ideally suited for multi-coincidence momentum spectroscopy. Using a 3-dimensional photoelectron/ion momentum spectrometer (reaction microscope or REMI [11]) along with attosecond pulses allows to temporally resolve combined electron and nuclear dynamics, by means of kinematically complete measurements on their natural time scale.
Attosecond beamlines with high-repetition-rates for photoelectron spectroscopy exist and have been reported in [10,12–15], with Ref. [10] even demonstrating the ability to perform coincidence measurements. XUV attosecond beamlines (based on Ti:Sapphire systems) combined with a REMI exist as well and have been reported in [16], [17] and [18]. All these systems lack either the ability to study processes with low cross-sections due to their repetition-rate (latter case) or from providing complete momentum information for both ions and electrons (former case).
Although Ref. [10] presents ion-electron coincidence measurements with a high-repetition rate laser, their effusive target limits the ability to perform ion momentum spectroscopy. In our setup, we have a target that is cold (<5K in the jet direction and $\approx$100 mK in the perpendicular direction) and dilute, which provides us with excellent resolution for ion momentum spectroscopy. This is seen in the results presented in Sec. 4.1, showing joint energy distributions obtained from ion and electron momenta. We therefore present kinematically complete measurements using a high-repetition rate attosecond source in combination with a REMI.
The generated XUV attosecond pulses reach photon energies up to 40 eV. The beamline comprising an interferometer is used to perform XUV-IR pump-probe measurements on noble gases and molecules. Results from RABBITT [1] measurements on argon and H$_{2}$ demonstrate the capabilities of the setup. In addition, we present an upgrade to the system with the goal to perform multi-color pump-probe measurements, demonstrating the high stability of the attosecond beamline.
2. Experimental setup
This section describes the experimental setup in detail (shown in Fig. 1). It consists of four main parts: the driving laser, the HHG source with the interferometer, a focusing element and the reaction microscope (REMI). The section ends with a description of the active phase-stabilization of the interferometer.
Fig. 1. The constituent parts of the attosecond beamline: The CPA laser, the XUV-IR interferometer and the HHG chamber, toroidal mirror chamber and the differential pumping stages connected to the reaction microscope (REMI).
2.1 Driving laser
A commercial laser from AFS (ActiveFiber Systems GmbH, Jena) is the front-end of the attosecond beamline. The laser system comprises a fiber-based Chirped Pulse Amplifier (CPA) [19] which works on the coherent combination of several phase-locked individual amplifiers as explained in Refs. [20–22]. The CPA delivers pulses with a duration of approximately 250 fs ($\mbox {sech}^{2}$ fit), 2 mJ pulse energy. To reduce the pulse duration, the pulses are coupled into an argon gas (2 bars) filled hollow-core fiber (HCF) [23]. The spectrally broadened pulses are temporally compressed to approximately 40 fs using chirped mirrors, with a pulse energy of 1 mJ. For further pulse compression, the output of the first HCF can be coupled into a second HCF, bringing the pulse duration down to approximately 8 fs. All the experiments presented in this paper were performed with 40 fs pulses. These pulses are steered to an interferometer for XUV-IR pump-probe experiments. The laser has variable repetition rates - 49 kHz, 75 kHz and 147 kHz. The pulse energy is unaffected by choice of the repetition rate and all experimental results presented here were obtained using a repetition rate of 49 kHz. This repetition rate was chosen to ensure that all the ions of interest have a time-of-flight that would be less than the time between two consecutive IR pulses, thereby simplifying the data acquisition. Moreover, the count rate of the ions/electrons was sufficient to acquire a statistically significant number of events for the various ionization processes.
2.2 Interferometer
The Mach-Zehnder arrangement is shown in Fig. 2. The incoming beam, 10 mm in diameter is split into two parts using a mirror with a 3.5 mm central hole (HMBS in Fig. 2). This results in a splitting of the beam into fractions of 85/15 (reflection/transmission). The beam path through the HHG chamber (reflected part) forms the pump (or ionizing) arm of the interferometer while the rest forms the probe arm.
Fig. 2. Schematic drawing of the interferometer including the HHG and recombination chambers. Legend: HMBS - holey mirror beam splitter, FL - focusing lens, NZ - gas nozzle, PC- differential pumping cone, DM - dump mirror, IR- iris, ALF - aluminium filter, RM - recombination mirror, PZT - piezo stage, DL - diverging lens.
The transmitted beam is reflected by a retro-reflector mounted on a piezoelectric translation stage, before it is diverged using a lens of focal length f= -25 mm in order to match the divergence of the XUV beam in the pump arm. The piezoelectric stage for delay control offers a step-resolution of 5 nm. The IR and XUV beams are collinearly merged by a recombination mirror (RM) which is again a mirror with a central hole (3.5 mm diameter).
2.2.1 High-harmonic generation
The reflected intense annular beam is focused with a lens of 50 cm focal length to a spot size of approximately 100 $\mu$m, right below the exit of a gas nozzle. The gas nozzle is mounted in a vacuum chamber and XUV radiation is generated through the process of HHG [4]. With a backing pressure of 700 mbar before the nozzle, the chamber pressure reaches about $9$x$10^{-3}$ mbar. The hole diameter of the cylindrical nozzle is $150~\mu$m.
The generated XUV radiation co-propagates with the annular driving IR radiation. The IR radiation is removed through several steps. First, after a distance of 50 cm from the HHG target, the XUV radiation that is located in the center of the IR beam is spatially separated with the help of an additional holey mirror (DM in Fig. 2). The intense IR beam is reflected by the holey mirror and guided to a beam dump outside the vacuum chamber in order to reduce the heat load inside the chamber. In addition, the beam transmitted through the holey mirror passes through an iris which cuts down the remaining IR radiation that might still surround the XUV beam. The iris is not actively cooled since the residual IR cut out by the iris does not cause any significant heating. Finally, an aluminium filter with about 200 nm thickness then filters out any remaining IR radiation along with the lowest order harmonics from the XUV beam. Using this annular beam method protects the aluminium filters from damage due to heating by the residual IR radiation that co-propagates with the XUV.
2.3 Toroidal mirror
The XUV-pump and IR-probe beams are together focused using a toroidal mirror (TM) (Fig. 3) onto a supersonic gas target inside the reaction microscope (REMI). The TM is designed in a way that it images both, the XUV source point and the virtual IR focus inside the REMI. The mirror has a $B_{4}C$ coating (30 nm thickness) on top of an aluminum layer (30 nm), which at a grazing incidence angle of $8^{o}$ is designed for high reflectivity of the XUV and IR wavelengths around 1030 nm. The total distance between the HHG source point and the gas-jet is 2.6 m. Under normal operating conditions, the pressure inside the mirror-chamber is in the order of $10^{-7}$ mbar.
Fig. 3. Schematic of the toroidal mirror mounted on four different stages. The lowest is a translation stage moving the whole mirror on the sagittal plane. Two goniometers in between are used to rotate the mirror along the Pitch and Roll axes ( Axes A and B respectively in the figure). The upper-most stage rotates the mirror around the Yaw axis (Axis C). Figure adapted from [24].
2.4 Differential pumping stages and reaction microscope
The toroidal mirror chamber is followed by a differential pumping stage since the REMI requires to be operated at a pressure of $10^{-10}$ mbar or below. The differential pumping stages create a smooth pressure gradient between the mirror chamber and the REMI from $10^{-8}$ mbar to $10^{-11}$ mbar.
The reaction microscope ( [11,25]) employs a supersonic gas-jet for target delivery and it can detect ions and electrons in coincidence (see Fig. 4). The gas jet is 1 mm in diameter at the focus of the XUV and IR. The target is internally cooled by supersonic expansion to a few Kelvins, thereby leading to a very narrow momentum distribution of the gas particles. This is achieved by taking a gas reservoir at room temperature ($\approx$ 300 K) with a backing pressure of a few bars and allowing it to undergo expansion through a 30 micron diameter nozzle (technical details from Ref. [24]) into a chamber with a few millibars of pressure. This leads to the formation of a gas-jet which afterwards passes through two skimmers with diameters of 150 $\mu$m and 200 $\mu$m. The distance between the nozzle and the reaction volume is 115 mm, while the nozzle-skimmer distance is about 7 mm.
Electrons and ions created in the center of the REMI by the interaction of XUV and IR beams with the gas-jet are guided to their respective MicroChannel Plate (MCP) detectors using co-axial homogenous electric and magnetic fields. The electric field used for accelerating the charged particles is between 3 - 12 V/cm and the magnetic field applied is between 4 and 10 Gauss, thereby providing a $4\pi$ acceptance for electrons with kinetic energies up to 22 eV and ions with kinetic energies up to 3 eV.
Along with the MCP detectors, Delay-line Anodes [27] provide the position of the electron and ion hits. The detection system therefore provides the time of flight of the charged particles and their respective hit positions on the detector. This enables a complete reconstruction of the momentum components (see [11]) of all charged fragments detected in coincidence.
In order to avoid false hits due to scattered light in the REMI that causes secondary electron emission, the XUV and the IR beams are dumped onto a slightly bent tubular extension at the end of the REMI.
2.5 Stability of the beamline
The beamline requires a high level of stability to measure photoionization time delays in the order of a few tens of attoseconds. Patricularly, the temporal jitter while performing delay scans should be less than about 100 attoseconds [28]. Additionally, interferometric drifts need to be minimized and compensated to perform measurements lasting several hours for targets with low ionization cross-sections. These requirements call for having an active-stabilization system with closed-loop control to reduce both the long-term drifts and short-term jitter. To achieve this, the interferometer is extended as shown in Fig. 5.
Fig. 5. Schematic drawing of the interferometer with drift stabilization. The extended part of the interferometer is in the region shaded green. Legend : HMBS - holey-mirror beam splitter, FL - focusing lens, HHG - HHG chamber, DM - dump mirror, ALF - aluminium filter, BS - beam splitter, PZT - piezo stage, DL - diverging lens, RM - recombination mirror, CMOS - camera.
A small portion of the pump IR beam that is reflected to the beam dump by the mirror DM, is picked up using a rectangular mirror and guided on to a beam splitter. Likewise, a part of the probe IR beam is guided through a hole in the recombination mirror (RM). By adjusting the spatial overlap of the beams, interference fringes are obtained on the camera which has an exposure time of 1/20th of a second. A narrow section of the image having the best fringe contrast is chosen and cropped. Integrating the cropped image along one axis gives the projection in the form of a sine wave. Figure 6 is a stack of the sine waves from images acquired every 10th of a second, over 1 hour. The phase of this sine wave is obtained using methods from Fourier Transform Interferometry [29,30]. At the beginning of the experiment, a reference image is captured and the phases of the fringes during the experiment is compared every $1/10$th of a second to this reference. If a phase shift is registered, an error signal proportional to the phase shift is generated in order to move the piezo stage to compensate the drift. This is conceptually the same as the method presented in Ref. [31].
Fig. 6. Top: Interference fringes of the free-running interferometer (left) and the stabilized interferometer (right) over a timeframe of 1 hr. Bottom: Corresponding phase and time delay shifts of the fringes over 1 hr.
Figure 6 shows the phase drift when the interferometer is free-running as well as when the interferometer is locked to one particular setpoint phase with the active stabilization. The phase of the free-running interferometer drifts by about $\frac {\pi }{4}$ radians after 60 min. Assuming no variation of the laser’s central frequency and using the relation $\phi =\omega _{IR}\tau$ ($\omega _{IR}$ - IR frequency, $\tau$ - time), this corresponds to about 400 attoseconds temporal drift. With active stabilization, the drift is negligible and only a short-term phase jitter of $0.03\pi$ radians ($\approx$50 attoseconds (RMS)) is observed (Fig. 6).
While performing pump-probe delay scans the setpoint phase is incremented in regular intervals and the piezo stage is moved accordingly. With an increase in the pump-probe delay, the contrast of the interference fringes gradually reduces and the fringes vanish for delays more than the FWHM of the pulse. To counter this, a band-pass filter is placed in front of the camera which lets only a narrow band of frequencies. As a result, the interference fringes are visible for a much longer delay range (100s of femtoseconds).
As seen in Fig. 7, a delay scan from 0 to 8.5 femtoseconds ($5\pi$ shift in phase) also has only a short-term jitter below 50 attoseconds (RMS). The phases from the interference fringes shown here therefore are a part of an ’in-loop’ measurement and may not completely mirror the phase shifts of the XUV-IR interferometer, since the actual interferometer has two additional components (ie. the recombination mirror and the toroidal mirror). The stability of the actual interferometer can be seen in the ’out-of-loop’ measurements explained in Sec. 4.2. The in-loop and out-of-loop measurements together indicate that XUV-IR pump-probe experiments can be performed with a sub-50 attoseconds stability.
Fig. 7. Top: Measured phases of the interference fringes along with their respective setpoint phases, Bottom: Errors in relative delay throughout the delay scan.
The slow drifts which typically occur over a few hours are very efficiently corrected by this method. The arrangement presented here is comparable to the one presented in [13] and demonstrates the ability to stabilize the interferometer without the need of an additional co-propagating CW laser for interferometric feedback, as reported in Refs. [10,12,31].
The primary temporal information in the experiments presented here is imprinted in amplitude oscillations of the photoelectron spectrum, with a time period of 1.7 femtoseconds (Sections 3,4). With interferometer drifts in the order of a few hundred attoseconds per hour, temporal information is lost when data is taken over a few hours, due to smearing out of the oscillations. Without the active stabilization, the dataset would require corrections to the phase after every 10 minutes to account for the drift. With the stabilized interferometer, data recorded even over a few hours do not need any further corrections.
Limitations manifest when a dataset is acquired over very long durations ($>12$ hrs). This can be seen with the measurements performed on argon (described in Sec. 4.2). While analyzing the delay-dependent photoelectron spectrum, a drift of 300 attoseconds was observed over 12 hours. This might be caused by a combination of factors such as instabilities in the laser performance (i.e. laser power and beam pointing instabilities), along with the inability to completely eliminate the effects of thermalization. For such long measurements, the dataset would need a correction, but only after 6-8 hours. The stabilization is also a vital element for measurements with oscillation periods less than 1 femtosecond (presented in Section 5.).
3. Characterization of the XUV pulses
3.1 XUV photon flux and spectrum
The XUV photons are generated in the HHG chamber as described in the previous section. The pulse duration of $\approx$40 fs ($\approx ~12$ cycles) of the fundamental IR field results in an XUV Attosecond Pulse Train (APT). The pulse energy is $0.75$ mJ. An estimation of the photon flux and spectral shape of the XUV radiation after it has passed through the aluminium filter, on the target inside the REMI is possible using the photoelectron spectrum. The XUV spectrum is obtained by adding the ionization energy($I_{p}$) of the target gas to the kinetic energies of the photoelectrons and by correcting for variations in ionization over the photon energies. Such a reconstructed photon spectrum for the XUV ionization of argon is shown in Fig. 8.
Fig. 8. Reconstructed XUV spectrum (after the Al filter) from the photoelectron spectrum of argon ($I_{p}=15.8 eV$). Cross section obtained from Ref. [33]. The area shaded green represents the harmonics chosen for the attosecond pulse train reconstruction.
For calculating the photon flux of the XUV radiation, the following formula is used:
The factors to be taken into account are: the photoionization rate $R$ (3 kHz), the target density ($n=10^{11}$ atoms/cm$^{3}$) of the gas inside the REMI, the interaction length L$= 1~$mm, the detection efficiency($\eta \approx 40~\%$) and the average ionization cross-section ($\sigma \approx$ 25 Megabarn). With these values for photon energies between 15-35 eV plugged into Eq. (1), we obtain an XUV photon flux in the order of $10^{11}$ photons/s which corresponds to $\approx 10^{7}$ photons/pulse. This value is comparable to the numbers reported in recent publications on HHG with a high-repetition-rate laser [12,32].3.2 Attosecond pulse train
The average duration of the pulses in the APT is estimated using the RABBITT method [34]. This method is based on photoionization of atoms or molecules using an APT. The frequency spectrum of an APT has a comb like structure, also called the harmonics. Thus, when an APT ionizes an atom, it results in discrete peaks in the photoelectron spectrum. The spacing between each peak is twice the IR frequency ($2\omega _{IR}$). Adding a phase locked IR field which also spatially and temporally overlaps with the XUV field, leads to the formation of sideband peaks (Fig. 9) in between the harmonics. The amplitude of these sideband peaks varies as a function of the time delay between XUV and IR pulses and are also called sideband oscillations. These sideband oscillations are the key feature of every RABBITT spectrogram.
Fig. 9. Top: Photoelectron Spectrum from the ionization of argon with XUV+IR, integrated over all delays. Bottom: Experimental RABBITT trace from the ionization of argon. The red dots in the top part are the sideband oscillation phases.
A cosine function of the form: $I_{sb} = A \mbox {cos}(2\omega _{IR} \tau + \Delta \phi )$ is fitted to each individual sideband oscillation. The phase term $\Delta \phi$ is approximated to be $\Delta \phi =\Delta \phi _{XUV}+\Delta \phi _{A}$ [35]. $\Delta \phi _{XUV}$ stands for the spectral group delay of the XUV pulses and $\Delta \phi _{A}$ is the atomic phase, which contains information about the atomic potential and the interaction between the IR laser pulse and the quasi-free electron in the continuum. Since $\Delta \phi _{A}$«$\Delta \phi _{XUV}$ [35], in this case, the atomic phase can be neglected and thus $\Delta \phi \approx \Delta \phi _{XUV}$.
Figure 9 shows a RABBITT trace that was measured by ionizing argon as a target gas in the REMI. The phases for sidebands 16 to 24 are also plotted in Fig. 9. From the phase difference between each sideband, the spectral phase of the APT is obtained.
The spectral amplitude of the APT is taken from the reconstructed XUV spectrum (Fig. 8). Knowing the spectral phases and the spectral amplitude of the APT, the structure of the attosecond pulses in time is reconstructed with the inverse Fourier transform. With this method, we obtain an average pulse duration for the XUV pulses in the APT as $410 \pm 30$ attoseconds. In comparison, the Fourier limited pulses in the APT would have a duration of $305$ attoseconds (Fig. 10).
Fig. 10. Reconstructed XUV pulses from the attosecond pulse train. The Fourier Limited pulses have a duration of 305 attoseconds while the retrieved pulses have a duration of $410 \pm 30$ attoseconds.
4. Multi-particle coincidence RABBITT measurements
Using the coincidence detection capabilities of the REMI, the various ionization channels in atomic/molecular photoionization can be studied through XUV-IR pump-probe experiments. Two examples of attosecond time resolved experiments - the photodissociation of the hydrogen molecule and the photoionization of argon dimers - are presented here.
4.1 RABBITT with H$_{2}$
Photoionization of molecules such as H$_{2}$ often reveal intriguing aspects of molecular dynamics and corresponding experimental datasets serve as platforms to test the latest theories. Through RABBITT measurements on such systems, it is possible to observe the coupling of electron-nuclear dynamics with attosecond precision, by studying dissociation processes [36]. The cross-section for the dissociation of H$_{2}$ is 2 orders of magnitude lower than direct ionization, as seen in Fig. 11, where the Time-of-flight spectrum for ionization by the APT and IR field is shown. The electrons are mainly from the direct ionization. Even with a high-repetition rate laser, the data must therefore be acquired over at least a few hours to obtain a significant number of events from the dissociation channel.
Fig. 11. Time of flight (TOF) spectrum for the ionization of H$_{2}$ by the APT + IR. The ratio of ionization yields from direct ionization to the dissociation channel ($\frac {N(H^{+})}{N(H_{2}^{+})}$) is approximately 0.06. Figure adapted from [24].
Using the ion and electron momenta provided by the REMI, high quality 2-dimensional joint energy distributions (e.g. Figure 12) can be obtained. In such a distribution, the ion Kinetic Energy Release(KER) [37] in molecular dissociation is plotted against the respective electron kinetic energy. With the help of joint energy distributions, the dissociation pathways can be identified.
Fig. 12. Bottom: A two dimensional joint-energy distribution of the KER vs electron kinetic energy for the dissociation of hydrogen in the presence of XUV and IR integrated over all delays. Top: Electron kinetic energy spectrum obtained by integrating over all KERs. Figure adapted from [24].
The joint energy distribution obtained by performing an XUV-IR pump-probe measurement on the H$_{2}$ molecule and integrating over all delays is shown in Fig. 12. By choosing narrow KER windows, electrons emerging from various dissociation channels are obtained. For each dissociation channel, plotting the electron kinetic energy as a function of time-delay gives the respective RABBITT spectrogram. Two such KER windows are shown in Fig. 12, corresponding to the Ground state dissociation and the Bond Softening channels. Ground state dissociation occurs when the molecule dissociates directly upon absorption of one XUV photon, while bond softening occurs when an IR photon couples the ground state of the molecular ion to the first excited state of that molecular ion after ionization by XUV [38]. The RABBITT spectrograms for these channels are shown in Fig. 13. Without being able to map the electron kinetic energies to their KERs, the total photoelectron spectrum would contain a mix of signals from all dissociation channels, due to which temporal dynamics cannot be reliably extracted.
Fig. 13. RABBITT trace for electrons from: Left - the ground state dissociation channel (KER = 0 to 0.38 eV in Fig. 12), Right - the bond softening region (KER = 0.5 to 0.85 eV in Fig. 12). Figures adapted from [24].
The KER distribution for ground state dissociation exhibits a maximum at zero and a tail towards larger KERs. For bond softening, the KER exhibits a broad peak with a maximum around 0.6 eV. Where both the KER distributions overlap, there is an interference between the two channels. This interference leads to an asymmetric electron emission with respect to the proton [39,40]. A detailed analysis of the sideband oscillations for the two channels along with the 3-dimensional momentum distribution of the fragments reveals that this asymmetric electron emission can be controlled on a sub-femtosecond timescale by varying the XUV-IR delay. This finding is also validated by a theoretical model. The results of this experiment are discussed in detail in a separate publication [41]. This experiment is extremely challenging with a conventional laser system (Rep.-rate <10 kHz) as such a multi-particle coincidence measurement would require a long acquisition time, in the order of a few days.
We note that for this measurement, the stabilization was not used. This was because the interferometer drift stabilization was still being developed while this measurement was performed and was hence not installed in the beamline. The signal to noise ratio was sufficient enough to resolve oscillations in a short time window of approximately 10 minutes, demonstrating good short-term passive stability. However, owing to long-term drifts, the dataset was later corrected in blocks of 10 minutes. The acquisition time for this dataset was around 15 hours.
4.2 RABBITT on argon
A RABBITT measurement was performed with the active stabilization on, to study the time resolved photoionization of argon dimers. While performing RABBITT on argon, a significant number of data points are also obtained from the ionization of argon dimers since the supersonic gas jet has a small but noticeable contribution of dimers. The fraction of coincidences detected from the argon dimer is only about $1\%$ of the coincidences detected from the ionization of atomic argon (Fig. 14).
Fig. 14. Time of flight spectrum of the ions for ionization with the APT and IR. The ratio of dimers ionized with respect to atomic argon is around $1\%$.
To eliminate false coincidences, the ion detection rate for the ionization of atomic argon was maintained at less than one-tenth of the laser’s repetition rate. With the Ar$^{+}$ ions being detected at a rate of 3 kHz, the dimer ions were detected at about 30 Hz. To obtain a statistically significant number of data points, the measurement was run over 12 hours, performing multiple delay scans. The measurements on argon are also the "out-of-loop" measurements to quantify the interfometer stability. Although stabilization was on, a small amount of drift was observed upon analyzing the RABBITT trace of atomic argon. This is because the phase shift in the interference fringes does not completely mirror the drift in the real interferometer as explained in Sec. 2.5.
The actual drift of the interferometer is obtained by analyzing the phase shift of one sideband with time. For example, the data taken over 1 hour is divided into four parts and the phase of the sideband is estimated for each RABBITT trace (Fig. 15). Keeping the sideband phase from the first part of the measurement as a reference, the phase shifts over one hour can be found. The mean drift over 1 hour obtained by this method gives a value less than 50 attoseconds. Along with the information from analyzing the interference fringes in Sec. 2.5, this clearly indicates that the XUV-IR pump-probe measurements are performed with a sub-50 attosecond stability. For the long term stability, the entire dataset over 12 hours was divided into 1 hour slices and the procedure above was repeated, the phase shift of the sideband was around 300 attoseconds ($\approx 0.2\pi$ radians phase shift) over 12 hours. This is because the drift is cumulative and cannot be fully eliminated by the feedback loop. The oscillation contrast in the RABBITT trace is however not significantly affected. The dataset hence did not necessarily require a drift correction, since the oscillation contrast is sufficient to retrieve the phases. The phases retrieved from the sideband oscillations for electrons in coincidence with Ar$^{+}$ and Ar$^{+}_{2}$ respectively, are shown in Fig. 16.
Fig. 15. Top : Projection of the sideband oscillations from a RABBITT measurement on atomic argon, tracked over 1 hour. Bottom: Phase shift of the sideband oscillations over one hour, obtained with the cosine fit described in Sec. 3.2.
Fig. 16. Top: Photoelectron spectrum integrated over all delays. Bottom: Experimental RABBITT trace for the photoionization of argon dimers. The green dots in the top part are the measured sideband oscillation phases for the dimers and the red dots are the phases from Fig. 9.
The phases measured in the case of dimers show negligible difference to that of atomic argon. The reason for this could be the weak Van der Waals potential that binds the argon atoms in the dimer. The electron wavepacket exiting such a loosely bound system experiences a phase shift that is mostly from the Coulomb potential of one of the atoms. Hence, the phases resemble the case of atomic argon. Further measurements with longer acquisition times are necessary for an accurate comparison as well as a deeper understanding of how a Van der Waals potential influences photoionization delays.
However, this experiment demonstrates the ability of the setup to reliably perform coincidence measurements over several hours or even days and also opens up the possibility of observing even the dissociation of argon dimers, such as in Interatomic Coulomb Decay [42]. The fraction of dissociated argon dimers is typically $10^{-4}$ times that of atomic argon, thereby requiring the experiment to be run for at least 48 hours, which is feasible with this system.
5. Towards multi-sideband RABBITT measurements
The photoelectron spectra in conventional RABBITT contain only one sideband in between the two adjacent high-harmonic bands. The sideband is formed by a two-photon transition process where the XUV photon causes a bound-continuum transition and the IR probe photon drives a transition within the continuum. Changing the ratio of the HHG-driving pulse frequency and the probe pulse frequency allows the number of sidebands between the two high-harmonic bands in the photoelectron spectrum to vary. The interfering quantum paths lead to the intensity modulation of the sidebands in the delay scan, involving different numbers of transitions in the continuum [43,44]. This opens an opportunity to study multi-photon transitions within the continuum.
In Ref. [43], a new multi-sideband RABBITT scheme has been proposed, that involves using the second harmonic ($\lambda = 515~nm$) of the laser frequency to generate the APT while keeping the fundamental IR beam ($\lambda = 1030~nm$) as the probe. Since subsequent harmonics are now separated by four times the IR photon energy, the RABBITT spectrum contains three sidebands instead of one. The modulation frequency for these sidebands is twice that of conventional RABBITT (thus $4\omega _{IR}$ and $\tau _{SB} = 850~as$). It is now essential to have a sub-50 attoseconds interferometer stability. We discuss here the two main modifications done to the setup to study 3-Sideband RABBITT, as shown in Fig. 17.
Fig. 17. Modified experimental setup for the Multi-Sideband RABBITT measurements. Note: DCM- dichroic mirror.
First, a telescope is placed in the pump arm to reduce the beam diameter to approximately 4mm. The collimated beam then goes through a BBO crystal, followed by a dichroic mirror to separate the fundamental and its second harmonic. A half-wave plate is placed after this in order to match the polarization of the second harmonic pump with the fundamental probe. The collimated second harmonic beam is expanded and focused on the HHG target.
Second, in order to operate the drift stabilization with this setup, interference fringes need to be generated on the CMOS camera. Owing to two different wavelengths of the pump and probe beams, an additional BBO is used to convert the probe IR beam transmitted through the recombination mirror (RM in Fig. 5), into its second harmonic. A half-wave plate is placed after this BBO as well to match the polarizations. Using the drift stabilization system, the interferometeric jitter in this case also is less than 50 as, and the $4\omega _{IR}$ oscillations in the 3-sideband RABBITT spectrogram are well resolved. Without stabilizing the interferometer, the oscillations are not visible, indicating that a very good stability is achieved in the former case. Figure 18 shows one of the first experimental RABBITT traces measured with this configuration. The $4\omega _{IR}$ oscillations are clearly visible not only in the center sideband, but also in the upper and lower ones with a good signal to noise ratio. Further analysis of the retrieved sideband phases along with other results of this experiment will be published elsewhere.
Fig. 18. Bottom: Experimental trace from a 3-Sideband RABBITT measurement on argon, Top: Photoelectron spectrum integrated over all delays.
6. Conclusion
The successful combination of a REMI with a high-repetition rate laser for attosecond pump-probe experiments is presented here. To demonstrate the capabilities of the setup, measurements have been performed with molecular hydrogen and argon dimers on the attosecond timescale. Both measurements lasted at least 12 hours, confirming the required stability for coincidence experiments. The experimental setup has been further modified for performing Multi-Sideband RABBITT measurements. Additionally, work is being carried out to extend the XUV cut-off in order to obtain photons with an energy higher than 50 eV, which would be crucial for studying processes such as single-photon double ionization in noble gases. This system provides a robust tool for performing new and highly demanding experiments that require high-stability, a high-repetition rate attosecond source and a kinematically complete detection scheme allowing data acquisition over days.
Funding
Deutsche Forschungsgemeinschaft (DFG-SPP-1840-HA-8399/2-1).
Acknowledgments
The authors would like to thank Sivarama Krishnan for valuable inputs while preparing the manuscript.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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